{-# LANGUAGE ExistentialQuantification #-}

import Control.Category
import Control.Arrow

-- data Kl' s i o = Kl' (i -> s -> (s, o))

data Kl i o = forall s. Kl (i -> s -> (s, o))

-- OK
instance Category Kl where
  id = Kl $ \ i () -> ((), i)
  (.) (Kl u2) (Kl u1) = (Kl u12) where
    u12 a (s1, s2) = ((s1',s2'), c) where
      (s1', b) = u1 a s1
      (s2', c) = u2 b s2
-- OK      
instance Arrow Kl where      
  arr f = Kl $ \i () -> ((), f i)
  first (Kl u) = (Kl u') where
    u' (i, x) s = (s', (o, x)) where
      (s', o) = u i s
      
-- Can't make this work.  The problem seems to be the same as before:
-- there's no way to require that the hidden types of both
-- constructors are the same.
      
instance ArrowApply Kl where
  app = Kl $ \((Kl f), a) -> f a